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If I factor $(n+1)/2n$ by $n$, I get $n(1+1/n)/n(2)$. Simplifying, I end up with $(1 + 1/n) / 2$.

This can be rewritten as: $1/2 + (1/n)/2$, which would give me $1/2 + (1/n) \times (1/2) = 1/2 + 1/(2n)$.

Why is this wrong? I'm told: $(n+1) / (2n) = 1/2 + 1/n$ ?

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    $\begingroup$ The fraction is $\frac{n+1}{2n}$? That is indeed $\frac{1}{2} + \frac{1}{2n}$. $\endgroup$
    – Daniel Fischer
    Commented Oct 16, 2014 at 17:18

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If your n+1/2n represents $\frac{n+1}{2n}$, then we have$$\frac{n+1}{2n}=\frac{n}{2n}+\frac{1}{2n}=\frac{1}{2}+\frac{1}{2n}$$ because $$\frac {A+B}{C}=\frac{A}{C}+\frac{B}{C}.$$

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  • $\begingroup$ Incredibly fast answers. I'm still trying to figure out how to write mathjax and you've already answered. Thank you! $\endgroup$
    – Sam
    Commented Oct 16, 2014 at 17:24
  • $\begingroup$ @Sam: You are welcome. $\endgroup$
    – mathlove
    Commented Oct 16, 2014 at 17:27
  • $\begingroup$ @Sam: consider upvoting and accepting if you are satisfied with the answer :) $\endgroup$
    – anderstood
    Commented Oct 16, 2014 at 17:57
  • $\begingroup$ @anderstood Upvoting requires 15 reputation and a registered account. Sam can't do that (yet, at least). $\endgroup$
    – Daniel Fischer
    Commented Oct 16, 2014 at 18:06
  • $\begingroup$ @DanielFischer: Ah OK, but can he accept? $\endgroup$
    – anderstood
    Commented Oct 16, 2014 at 18:09

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